help-0

[slender marten]

They're a troll. Their bio reads too nicely.

[vale wigeon]

and your question can be answered with a calculator.

<@&268886789983436800> underage

[next brook]

.close

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[lyric fable]

Help

[fierce prairie]

Do you know what similar triangles are?

[lyric fable]

yes

it could be similar by SSS

i think

[fierce prairie]

Yes

and there are 3 single lines on both triangles

[alpine sable]

All equilateral triangles are similar

If you take any side of either triangle and compare it to the other triangle you will have a constant ratio since, well, every side is the same

[lyric fable]

what about this one

[alpine sable]

Do you know what an equilateral triangle is?

[lyric fable]

yes

equal sides?

oops that was the weong one

wrong

[alpine sable]

I'm not really sure what that red arrow means afaik it isn't standard notation

[lyric fable]

i think it means parallel

the side is parallel

[alpine sable]

I recommend to you that you try to draw it out on a piece of paper and see what happens, you don't necessarily have to use exact angles

If you want a hint btw here you go:
||Consider ∠ECD and ∠GEF||

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[woeful wind]

how would you do part i?

I thought acceleration is written as dv/dt

I dont understand where they got v dv/dx from

[lone heart]

@woeful wind Has your question been resolved?

[woeful wind]

<@&286206848099549185>

[haughty sorrel]

Acceleration can also be written as vdv/dx

[weary torrent]

Idk if I’m right but the sum of forces are mg-mkv^2 or gravity - air resistance and if you multiply it by a the bottom cancels

[haughty sorrel]

a=dv/dt= dv/dx×(dx/dt)=vdv/dx

[weary torrent]

Mass already canceled

[woeful wind]

thank you that makes sense

[haughty sorrel]

Yes it is acceleration

[woeful wind]

yeah they both are

thanks for your help

.close

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[tall thunder]

Somebody help me with task.
4. Solve the Cauchy problem using the operational method

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@tall thunder Has your question been resolved?

[alpine sable]

Someone help him please

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[final badge]

Did i get number six right?

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@final badge Has your question been resolved?

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[alpine sable]

i need help

[scarlet oriole]

yall got the exam and now need help solving it all?

[alpine sable]

yea

i already have the answers

but i need a solution

cuz im gon explain it

[scarlet oriole]

yeah it's against the rules to solve this kind of stuff tho, if you have the exam and answers you at least can do some simple work and read the textbook to see how they get solved

[alpine sable]

this is not an examm

it's an assignment

[scarlet oriole]

same thing

you need to work on it yourself, if you have a notion related to probability that you don't understand then ask that instead no one will sit here with you solving each exercise

[alpine sable]

i just need like the solution plss

[scarlet oriole]

you wont be getting it here try somewhere else

[humble fog]

Why not be productive and actually ask for the process?

So you can do all of them yourself once you understand

[alpine sable]

okay

[lone heart]

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[molten jackal]

How would you evaluate the integrals between (2,4) and also how would you do (4,7) ?

[molten jackal]

<@&286206848099549185>

<@&268886789983436800>

oh wait sorry wrong tag

[arctic steeple]

don't ping moderators for math help

[molten jackal]

<@&286206848099549185>

[sly mantle]

you already pinged helpers

[molten jackal]

can I not ping more than once?

i just did it since no one's looked at the questions yet

[sly mantle]

not within such a short timespan like that

helpers are volunteers so theyre sometimes just not available or not in the mood

[molten jackal]

.close

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[grizzled zephyr]

I an literally stuck

[grizzled zephyr]

In this lesson because of this

The slope in the quadratic

Is increasing

Why so i put it decreasing

In the derivative graph

The pink line

[soft saffron]

slightly confused to the actual question here

[alpine sable]

are u asking why the derivative's graph looks like that? @grizzled zephyr

is that your question?

[grizzled zephyr]

Yes

[grizzled zephyr]

The pink line

In the quadratic function

Is increasing

Why do we put a decreasing line in the derivative function

[alpine sable]

First and foremost, the derivative of a quadratic function is always a linear function

[grizzled zephyr]

I hope that is more clear

[grizzled zephyr]

I know this

But i wanna know why

[alpine sable]

Secondly, you are thinking about it wrongly

The collection of the tangent lines' slopes for the quadratic function makes up the derivative function of the original function you have

You are thinking about the slope of the derivative's graph

But in that case, you are examining the second derivative of the function

What you need to be looking at is where the y values are positive or negative

Positive y values in the derivative graph would indicate the function has a positive slope in that section of the function

[grizzled zephyr]

Oh

So a positive slope in the orginal function

Means postive y values

In the derivative function?

[alpine sable]

Yep

[grizzled zephyr]

@alpine sable

[alpine sable]

You got it

[grizzled zephyr]

Thanks alot

But why is that

Like the reason we evaluate it like this

[alpine sable]

Well like

What is a derivative?

[grizzled zephyr]

Tbh

Idk

I think this is my problem woth math

Idk really know what am studying

Anyways

Could u tell me

@alpine sable i think u forgot me

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[quaint bronze]

Hello how can I become better at maths? I love the subject but suck at it. Any studying tips or whatever would be greatly appreciated:)

[mortal trellis]

practice

[gusty gorge]

probably one of the biggest reasons why some people suck at math is they try to move too quickly

[pale kestrel]

You might think you suck

but thats often a misevaluation if at a highschool level

[gusty gorge]

take your time, and don't think that you have to keep up with whatever they're teaching now if you'd rather review stuff in the past

[pale kestrel]

Even if your teachers think u suck, id say the same. More often than not people 'suck' at hs math due to not so good teaching. Or teaching style that doesnt suit.

So for me, I'd find other sources to learn from or support what im learning in school

khan academy, tutor, etc.

[quaint bronze]

I am in high school(adults)

Yea my teacher giving up on me… I just asked her if could have more exercise to get better and she refused. She told me to re do over and over the same exercises

[pale kestrel]

sounds like lazy teaching

[quaint bronze]

I thought the same thing

Do you guys know any good sites where I can practice?

[pale kestrel]

khan academy

[quaint bronze]

I’ll check it out thank you so much!

[gusty gorge]

also if you're struggling in some math class

sometimes it really helps to go review the stuff from beforehand

instead of pounding your head at the problems in this particular class

if you have foundational gaps in your knowledge, then they will make learning further material very difficult

one way you can sorta diagnose this is if you go onto something like Khan Academy, start really low, and see when you struggle to answer the questions quickly and easily

[quaint bronze]

Sounds like a good method. I will do it right now, thank you.

.close

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[merry cave]

what percentage of the can is filled if you pour in the water from the glass
the glass is 1,5 dl
the can has 2 liters space

[prime bay]

How do i solve 1 and 2 in IX)

[merry cave]

.close

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[vale bridge]

Hi I'm trying to solve this with ratio test

To see if it converges or diverges

But I'm stuck here because I get 1^infinity

I think I would have to do lhopital rule somehow but I dont know how

[pallid scarab]

ok, so first of all, do you know about the obscure definition of euler's number?

[vale bridge]

I dont think ive heard of it

[pallid scarab]

are you using the ratio test $\sqrt[k]{|a_k|}$?

[ocean seal]

rafilou2003

[vale bridge]

Yes

And taking that as the limit of k goes to infinity

[pallid scarab]

alright

so, here's a hint

you can write a^x = exp(xlna)

[vale bridge]

I dont understand this

The notation

[pallid scarab]

$a^x = e^{xlog(a)}$, with $log$ the natural logarithm

[ocean seal]

rafilou2003

[vale bridge]

Theres no way

I think i'm too dumb for this

[alpine sable]

(a series converges only if the summand converges to 0. You've found that it converges to 1)

[vale bridge]

I dont understand this

But also I didnt find that it converges to 1

I have 1^infinity which could be 1 or it could be infinity

[alpine sable]

either way, its not 0

https://en.wikipedia.org/wiki/Nth-term_test

[vale bridge]

Oh thats divergence test

I think by that I would still get 1^infinity

Which is still indeterminate

[pallid scarab]

yes, you could use that the limit is bigger than 1

which is enough

[vale bridge]

Oh

So even though its indeterminate

It is either 1 or infinity and neither are 0

So it diverges

Is that it

[pallid scarab]

well it's between 1 and infinity

[vale bridge]

Why would it be between

[pallid scarab]

giving you the example I was talking about

$\lim_{n\rightarrow \infty} (1+\frac{1}{n})^n = e$

[ocean seal]

rafilou2003

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[jagged forge]

What is this asking for?

[jagged forge]

I keep entering different simplifications of the limit I made

[pallid scarab]

what have you done so far?

[jagged forge]

I just got it by guessing

It’s (n+5) / (n+1)(n+4)

[pallid scarab]

yes, doesn't this work?

[jagged forge]

Yes that was it

So I guess what they meant is remove the factorials?

[pallid scarab]

yes, because factorials could be simplifed

[jagged forge]

Ok sweet

[jagged forge]

This is kinda annoying. No class before this have gone over factorials but I’m just expected to know how to work w them I guess

It’s not too bad I just don’t like when classes skip things

Thanks again

[pallid scarab]

no problem

it's always important to remember that (n+1)! = (n+1)n!

[jagged forge]

Right. Thanks.

.close

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[restive sail]

this i part of statistics and expected results, the correct formula would be (n/k) * p^k * (1-p)^(n-k)
i dont understand how i need to use the product symbol
the solution given by the paper is: a = 0,41 and b = 100-k
i suspect there is an invisible multiplication dot after the E but I'm confused by the 1- at the start

[restive sail]

and the question was, with what to replace a and b

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[uncut galleon]

really struggling with this question

[slender quiver]

!status

[lone heart]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[uncut galleon]

1

[slender quiver]

can you visualize what the cut out would be

[uncut galleon]

i’m trying to draw a picture but i cannot figure out a way to make equal squares and i don’t know how to find the max # of squares

[slender quiver]

there is 4 squares you cut off

[uncut galleon]

ohhhh oh oh oh

i see… okay now i can visualize it

but i still am not sure how i would find what it’s looking for

<@&286206848099549185>

<@&286206848099549185>

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@uncut galleon Has your question been resolved?

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[north hemlock]

For this problem, I'm having issues trying to figure out a starting point

[north hemlock]

I feel like if I bruteforce it, I can get the answer eventually but I don't see the.... "correct" approach

[merry depot]

use the mods

You have what a is in terms of y0, y1, and y2
and you know a = 12 (mod 44)
what happens when you mod that equation by 44?

[north hemlock]

I'm left with $y_0$?

[ocean seal]

Juke | ping me if no response

[north hemlock]

wait

no

i'm left with....

35 + y_0?

wait oops duh bc it's multiplied so that doesn't make sense

okay so that means that y_0 is 12

[merry depot]

so you have a = y0 = 12 (mod 44)

Now, do the same thing for 35

[north hemlock]

so I get y_1 = 8

then I do mod 3 ...

$a=(12+44(8)+44(35)y_2)\mod 3 \equiv 0$

[ocean seal]

Juke | ping me if no response

[north hemlock]

,calc 44*8

[ocean seal]

Result:

352

[north hemlock]

10 mod 3 is 1 so 352 mod 3 is 1

,calc 352 mod 3

[ocean seal]

Result:

1

[merry depot]

howd you get 8?

[north hemlock]

I did...

$$a=(12+44y_1+44(35)y_2)\mod 35\equiv 20$$
$$\implies 12+y_1=20 \implies y_1 = 8$$

[ocean seal]

Juke | ping me if no response

[merry depot]

so, what happened to the 44 multiplied to the y1?

[north hemlock]

oh wait

,calc 44 mod 35

[ocean seal]

Result:

9

[north hemlock]

so I should have $12+9y_1 =20$

[ocean seal]

Juke | ping me if no response

[merry depot]

yes

[north hemlock]

so y_1 is 8/9

[merry depot]

right idea. but 1/9 isn't an integer

[north hemlock]

,calc 12 + 44(8/9)

[ocean seal]

Result:

51.111111111111

[merry depot]

division isn't a thing in mods

[north hemlock]

that's fine

oh shoot

[merry depot]

you can multiply by the inverse in Z35 though

[north hemlock]

mmmm

not sure what that means tbh

I suck at modular anything

[merry depot]

there's an integer in Z35, so that 9x = 1 (mod 35)

[north hemlock]

oh okay

that should be easy enough

lemme see..

well

hold on

shouldn't I be solving for 9x = 8 mod 35?

[merry depot]

you can

[north hemlock]

wym

,w 9x = 8 mod 35

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Jukelyn#0001

[north hemlock]

hm

[merry depot]

Smaller example. Think of this. 2x=3 (mod 5)
I can find x directly by brute force.
or multiply by the inverse of 2 (mod 5)
I know 2*3 = 6 = 1 (mod 5)

[north hemlock]

how do I know the inverse of a number mod 5

well

[merry depot]

so to solve 2x=3 (mod 5)
i do 3(2x) = 3(3) (mod 5)
so x = 9 = 4 (mod 5)

[north hemlock]

ahh

so for 9x = 8 mod 35
that'd be
72 = 64mod35
and 72 mod 35??

,calc 72 mod 35

[ocean seal]

Result:

2

[north hemlock]

what the fu-

wait..

I did something not right

[merry depot]

so you need to find the inverse of 9 mod 35

what multiple of 9 is 1 mod 35?

[north hemlock]

it'd be hmm

9 18 27 36

so

4

[merry depot]

yeah. So multiply 9x = 8 (mod 35) by 4

[north hemlock]

,calc 8 * 4

[ocean seal]

Result:

32

[north hemlock]

ahhh that's where 32 comes from

alright I see

is there a better way to do this?

[merry depot]

depends. that's one way.
I'll look at the mod sometimes

1 mod 35 is 1, 36, 71, ....

[north hemlock]

oh right

just add 35 a bunch

[merry depot]

yep

[north hemlock]

okay yeah taht makes sense

so then for my question

[merry depot]

so, you have y0 and y1, now do the same thing again to find y2

[north hemlock]

,calc 44*32

[ocean seal]

Result:

1408

[north hemlock]

,calc 5 +8

[ocean seal]

Result:

13

[north hemlock]

wait a damn sec

,calc 12 + 32(44)

[ocean seal]

Result:

1420

[north hemlock]

1420 mod 3 is like...

2?

,calc 1420 mod 3

[ocean seal]

Result:

1

[north hemlock]

oh shit

,calc 44(35)

[ocean seal]

Result:

1540

[north hemlock]

,calc 1540 mod 3

[ocean seal]

Result:

1

[north hemlock]

o

y_2 is jsut 1

so $y_0=12, y_1=32,y_2=1$

[ocean seal]

Juke | ping me if no response

[north hemlock]

,calc 12+32(44)+(44)(35)

[ocean seal]

Result:

2960

[north hemlock]

2960 is a

lemme make sure I didn't mess up...

,calc 2960 mod 40

[ocean seal]

Result:

0

[north hemlock]

FUCK

THAT'S NOT 12

,calc 2960 mod 35

[ocean seal]

Result:

20

[north hemlock]

that's fine

,calc 2960 mod 3

[ocean seal]

Result:

2

[north hemlock]

that's also wrong

so I messed up somewhere

[merry depot]

if it helps

,calc 44 mod 3

[ocean seal]

Result:

2

[merry depot]

,calc 32 mod 3

[ocean seal]

Result:

2

[merry depot]

,calc 35 mod 3

[ocean seal]

Result:

2

[north hemlock]

oh I did mod 3 wrong lol

,calc (32*44) mod 3

??

[ocean seal]

Result:

1

[north hemlock]

wait right..

then it's

,calc (44*35)mod 3

[ocean seal]

Result:

1

[north hemlock]

wtf

okay so I have $(12+32(44)+44(35)y_2) \mod 3 = a$

[ocean seal]

Juke | ping me if no response

[north hemlock]

so then

that = 0 as well

[merry depot]

yeah

[north hemlock]

but 12mod 3 = 0

32(44) mod 3 is 1

44(35) mod 3 is also 1

[merry depot]

yes

[north hemlock]

so I'm just left with $1+1y_2 = 0$

[ocean seal]

Juke | ping me if no response

[north hemlock]

ahhh

so y_2 = -1

weird, I wrote these but solved wrong somehow

[merry depot]

which is what in Z3?

[north hemlock]

2?

[merry depot]

yes

[north hemlock]

lit

,calc (44)(35)(2)+32(44)+12

[ocean seal]

Result:

4500

[north hemlock]

,calc 4500 mod 3

[ocean seal]

Result:

0

[north hemlock]

,calc 4500 mod 40

[ocean seal]

Result:

20

[north hemlock]

that should be 12

:/

,calc 4500 mod 35

[ocean seal]

Result:

20

[north hemlock]

oh typo oops

,calc 4500 mod 44

[ocean seal]

Result:

12

[north hemlock]

okay lit

that was intersting

thanks !

,calc

[ocean seal]

Please give me something to evaluate.
See ,help calc for usage details.

Apr 5, 2023, 1:02 AM

[north hemlock]

.close

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[lone heart]

@royal quest Has your question been resolved?

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[summer mauve]

I’m lost again😭

I think 3 is substitution

<@&286206848099549185>

[fierce prairie]

Yes

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[summer mauve]

And I have 6 as corresponding

I’m trying to figure out the rest

Like I know you have to subtract the 127 from 180 and that would get 53 which is equal to angle 1 but idk how to put that into a proof.

[lone heart]

@summer mauve Has your question been resolved?

[summer mauve]

<@&286206848099549185> y’all I’m sorry for a second ping buts it’s almost been an hour😭

[open fern]

@summer mauve

[summer mauve]

Yes thank you

[summer mauve]

Thank you for responding I’ve been waiting a long time

[open fern]

You are welcome

Angle 3 and angle 2 are linear pairs right?

[summer mauve]

Yes

Also supplemtary

Idk the teacher accepts both

[open fern]

The "supplementary angles" would be a safe statement to write

[summer mauve]

Okay

I’m just kinda confused on what reasons to put for 4 and 5

[open fern]

Angle 3 and angle 1 are corresponding angles

And corresponding angles are always congruent

[summer mauve]

So put that for 5 or 6?

Because idk what I would put for 6 other than definition of congruence

Wait maybe 5 for corresponding and 6 for congruence?

[open fern]

Ignore 6 for now

[summer mauve]

Okay

[open fern]

Let's write 5 first

[summer mauve]

Okay, corresponding angles, correct?

[open fern]

Yeah

[summer mauve]

Ok

[open fern]

If corresponding angles are congruent, the lines are parallel

[summer mauve]

Okay

[open fern]

So for the 6 it would be
Corresponding angles are congruent

[summer mauve]

Okay

So 4 is left

[open fern]

Do you feel satisfied?

[summer mauve]

That’s the most confusing one

Yes

Thank you

[open fern]

To calculate angle 3 from the equation, we have used the subtraction property of equality

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality.

[summer mauve]

Dude your smart, I really appreciate you helping me.

[open fern]

Thank you for your words

You are smart too

Just by giving hints

You get it

[summer mauve]

Alright then I’m gonna head to bed, thanks again!

.close

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[vital forum]

uhm help with this please

[lone heart]

@vital forum Has your question been resolved?

[vital forum]

i have an example here but its vague to me hope anyone can help

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[ocean seal]

infi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[short wave]

does this mean? for every y in B , there exists x in A , such that f(x) = y

[vale wigeon]

the $\ni$ feels out of place, though some books actually use it that way

[ocean seal]

Ann

[short wave]

yeah that's what confuses me

some books use \ni as such that

[vale wigeon]

yeah tbh prefer a colon or "s.t."

[short wave]

but does it mean such that here ?

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[orchid parrot]

integration of sin2x.sin4x.dx

[orchid parrot]

my answer comes -sin2x/4 +sin6x/12 +c

<@&286206848099549185>

[wind cloak]

seems correct

[orchid parrot]

but answers says wrong

my answers sheet even

@wind cloak

please

[wind cloak]

oh yeah your minus is in the wrong place my bad

[orchid parrot]

how so i dont understand formula is correct

• and - will multiply

as the formula

and gets plus

[wind cloak]

$\cos A - \cos B = 2\sin (\frac{A + B}{2}) \sin (\frac{B - A}{2})$

[ocean seal]

NEONPerseus

[wind cloak]

This is the formula

[orchid parrot]

i used the formula of 2sinasinb=cos(a-b)-cos(a+b)

@wind cloak

[wind cloak]

its the same thing right

[orchid parrot]

nope then why didnt it come

bro

@wind cloak

[wind cloak]

clam down with the pings

[orchid parrot]

ok i am just busy

kindly give me the answers fast i know i am being rude but please

[wind cloak]

its right I looked it up

[wind cloak]

you already have the answer lol

[orchid parrot]

why didnt it come

my plus and minus

[wind cloak]

I think you might've applies it wrong

[orchid parrot]

@wind cloak

[wind cloak]

$$

[orchid parrot]

??

@wind cloak

[wind cloak]

$\int \cos x \dd{x} = \sin x + C$

[ocean seal]

NEONPerseus

[orchid parrot]

Bro

This is the formula of cosmx

[wind cloak]

why have you added a negative sign

$\int \sin x \dd x = -\cos x + C$

[ocean seal]

NEONPerseus

[wind cloak]

You're confused with this one I suppose

[wind cloak]

$\int \cos mx \dd{x} = \frac{1}{m} \sin mx + C \neq \frac{-1}{m} \sin mx + C$

[ocean seal]

NEONPerseus

[orchid parrot]

Bro

There is another math i did

It showed the right answer

Wait

Okk thanks

[lone heart]

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[vale fjord]

I dont quite understand how to solve this?

[vale fjord]

I am just confused by what the question is asking

Please @ me

[leaden dagger]

n(U) = 200
n(A’ ^ B’ ^ C’) = 25
n(A’ ^ B ^ C’) = 15
n(A ^ B) = 20
n(A^ B’ ^ C) = 10
What is n(A) n(B) n(C)?

[vale fjord]

bro what?

[leaden dagger]

Venn Diagram

[vale fjord]

is that response supposed to help me with my question?

[leaden dagger]

no

[leaden dagger]

i dont care about your question

[vale fjord]

lmao my guy then make ur own help channel

get out of mine bro

[alpine sable]

is k a function of x or just a constant

ig a constant

[vale fjord]

i figured it out, i thought it could be any constant but the answer was 6

cuz u do algebra and to the top function and get x + 3 and substitue 3 for x and get 6

.close

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[sullen jungle]

Need to solve this equation not using a calculator:
sin x = sin 2x + sin 3x

[sullen jungle]

iv tried using the sum-to-product formula

and a few other things

but get stuck

the answer is supposed to be 74/7

[lone heart]

@sullen jungle Has your question been resolved?

[sullen jungle]

<@&286206848099549185>

[limpid wagon]

try expanding the sin3x using the sum of angles identity

[subtle birch]

use formulas of sin2x and sin3x

sin3x= 3sinx-4sin^3x

sin2x=2sinxcosx

[sullen jungle]

ill try

[alpine sable]

can someone help to differentiate it

[lone heart]

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[dreamy compass]

Hello, I'm stuck on trying to evaluate 3log base 3 of 9

[dreamy compass]

Not sure where to start with the 3 in the front

[vapid shuttle]

logarithms are asking a question. log base 3 of 9 is asking you, 3 raised to what power equals 9?

so what is log_3(9) then?

then multiply that by 3

[dreamy compass]

2

[dreamy compass]

oh

[dreamy compass]

don't know why that took so long to send

found an error in my other problem thanks to that

could you clarify a little more

still a bit confused

is there some property to be used here

first time seeing this kind of expression on a homework

[dreamy compass]

oh my god how did i not realize the 3 was being raised to the log

i got 9

is that right? @vapid shuttle

and 3.2 for #12

[vapid shuttle]

looks good to me

[dreamy compass]

thank you!

.close

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[drifting tiger]

why is 12.25 rounded off to 3 significant figures 12.2 but 12.35 rounded off to 3 significant figures 12.4

[cinder tundra]

Context

[lone heart]

@drifting tiger Has your question been resolved?

[prime badge]

rounding towards an even number instead of always in the same direction

makes the "total" error across many roundings smaller

[drifting tiger]

so for an even number it just stays the same and for an odd number it increases?

[prime badge]

yeah

[drifting tiger]

ight thanks a lot

[prime badge]

specifically when you round a 5

[drifting tiger]

gotchu

thxx

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[placid swallow]

I have the following system, I need to get a base and the dimension.

So far I managed to do gauss elimination and figure out that the dimension is 2 (n of variables - rk(a))

i set x1 = t but I feel like I'm going circles lol

do I need to introduce another parameter?

cause i end up w this which is not right

[lone heart]

@placid swallow Has your question been resolved?

[placid swallow]

there u go

[pine fable]

x_3 should be -t+2y

But otherwise it's correct

@placid swallow

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@placid swallow Has your question been resolved?

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[marble forge]

find x

[pine kettle]

!status

[lone heart]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[marble forge]

1

[hard patio]

okay there are two ways of doing this, the first one is to realise that triangle SRT is similar to AUT

so the ratio between the corresponding sides will be constant

[marble forge]

so
x+2:3x-3+x+2 = 6:14
?

[hard patio]

yes

(x+2) : (3x-3+x+2) = 6:14

[marble forge]

is the answer 3.4?

I don't know if I'm right or not

[hard patio]

looks alright to me

[marble forge]

wow tnx

tnx

.close

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[misty pivot]

hi

[misty pivot]

need help with inverse matrix 4x4

casio does all good

[vale wigeon]

by hand?

[lone heart]

@misty pivot Has your question been resolved?

[misty pivot]

no sorted. answer just gave result n was confused as online calc was diff but casio same

[lone heart]

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[placid tiger]

how would I approach this?

[sour verge]

Could probably use product sum formulas

[placid tiger]

i am not familiar with that can you elaborate

[median oar]

Isn’t that some identity

Sin 𝛂 cos 𝛃 - cos 𝛂 sin 𝛃

[sour verge]

Oh yeah I think so you're right

[median oar]

Isn’t that like cos 𝛂 - 𝛃 or something

Nope it’s sin 𝛂 - 𝛃

Close enough

Haha

[sour verge]

Yeah that's it

[next chasm]

Sin5xCosx = (sin6x + sin4x)/2
Cos5xSinx = (sin6x-sin4x)/2

[placid tiger]

thank you that makes it easy now

[median oar]

👍

[next chasm]

You can simplify and get sin6x dx

[median oar]

Remember your identities!

They are giga important for doing integrals

Don’t have to remember exactly what the identity is (definitely helps if you do) but know it exists

[placid tiger]

.close

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[void agate]

Here is a math question and it's solution.

I found this solution online, I worked the whole thing out on paper and the answer (8.0 cm) matches with the mark scheme.

I don't understand why the formula stated (above the numbers in the image) works for this. Can someone please explain to me why?

The main question I have: why do we work with volumes when the question explicitly states the clay is wrapped around the curved surface area?

[alpine sable]

The formula for the pyramid and sphere's volume?

[void agate]

Nah I meant the pink text

[alpine sable]

Oh

[void agate]

Why can we use this to find the answer

[alpine sable]

Because the thickness of the clay is 1.5cm

It's like a shell

[void agate]

why do we work with volumes when the question explicitly states the clay is wrapped around the curved surface area?
(i added this on)

[alpine sable]

Because the surface area not has a thickness of 1.5cm

If that makes sense?

Ohh mb

It's 500 because it's 500cm^3

that's volume

[void agate]

Of course

But why can we use volume 😭 It says in the question the 500cm^3 of clay was wrapped around the surface area... so why can we take the larger volume minus the smaller volume to equal 500 cm^3. That's the volume of the clay, not the surface area of it

I hope my question here makes sense, but this is what I dont understand

[alpine sable]

Imagine cutting out a circle from a larger circle

The larger circle has area $\pi R^2$

[ocean seal]

hannibal

[alpine sable]

the smaller $\pi r^2$

[ocean seal]

hannibal

[alpine sable]

so to get that area

You subtract the larger area from the smaller area

Get it?

[void agate]

Yeah! That makes absolute sense

[alpine sable]

Ok

So what's left over is the yellow

Same as here. You just subtract volumes, so the difference is what's left

[void agate]

Ohhhhhh

My god. That was so simple

[void agate]

The question is pretty much asking for the volume of this shape

The yellow

Man I was makin it complicated for no reason

Thank you so much @alpine sable

.close

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[nimble latch]

I am not sure how to approach this problem. I tried drawing it out but it was to no avail

[nimble latch]

.close

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[tight thunder]

guys

im looking at this for 24 hours i cant understand why the equation is set up this way

if first price is 10 and quantity demanded is 50

and when price is 20 quantity demanded is 10

why is equation set up like this

i understand the 10-50/20-10 part gives the slope but other i dont get

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@tight thunder Has your question been resolved?

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[void agate]

Why is the answer 25-x? And not x-25?

[haughty sorrel]

Number of students passed mathematics and English= students passed all three + students who passed only mathematics and English

[void agate]

x = passed all 3
25 = only math and english

x+25?

I'm sorry, I don't quite follow your explanation

[haughty sorrel]

This 25 will include the students who passed all of the 3 subjects and students who have passed mathematics and English but not science

So the answer will be 25-x

[void agate]

Oh my god I'm so stupid 😂

I just understood what you mean it was so simple

Thanks @haughty sorrel

.close

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[terse warren]

Is that posible to calculate angle C if BD is a bisector?

[terse warren]

Known info:
x = 45
Angle ADB = 55
DBC = 80

[void agate]

Yes

Since BD is a bisector, ADC is also 55 degrees (if BDG is a straight line)

Then you can do the rest

[placid blaze]

• BDC is also 55 degrees

[void agate]

Yeah thats what I meant mb

[terse warren]

Ok thanks

.close

[lone heart]

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[sullen haven]

Hello I'm learning combinatorics now and have this question:
In a class there are 3 benches, on each bench there are 10 places to sit. how many ways there to sit down 29 students ,if Dani and Rami both will need to sit on completely full bench (meaning that there no more free spaces) and between them there will be two other students?

I tried to think of Dany,Rami and the two between them as single unit but got stuck afterwards

[lone heart]

@sullen haven Has your question been resolved?

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@sullen haven Has your question been resolved?

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[gray patio]

some1 help me. im extremely new to this no idea wat even log is

[scarlet oriole]

Google log definition then

[velvet cliff]

I did it for you 😊

[gray patio]

wat

some1 give me an example

[scarlet oriole]

log is a mathematical operation that takes 2 inputs base and argument in your base base is 1/9 and argument is 3, this operation will output the power that takes 1/9 to 3

log of 100 with base 10 is 2

since it takes 10 power of 2 to go 100

what power you need on 1/9 to get 3 that's your question

[gray patio]

can you explain it in a more simple way

im middle school

[scarlet oriole]

can't get simpler than then

[velvet cliff]

rather ask what's not clear

[modern sedge]

log base a of b means: To what power do I have to raise a to get b?

[scarlet oriole]

read what i said slowly and process each word

[gray patio]

ok

so log of 25 with base 5 is 5 r

?

[modern sedge]

why 5?

[gray patio]

no

I mean 2

[modern sedge]

yep

[ocean seal]

MathIsAlwaysRight

[gray patio]

ehhh

[velvet cliff]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/introduction-to-logarithm-properties

it appears you're new to logarithms, so just watch this course

[gray patio]

how to solve it wen the base is not square root of the number

[magic bison]

Simple answer is5

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[modern sedge]

There are some logarithm rules that can simplify the expression

[gray patio]

no dont care abt the thing after log5,20

[magic bison]

Ok for that you need to have log tables

[modern sedge]

log_5(20) itself has to be computed using calculator

[gray patio]

wat

[modern sedge]

it will be some awful horrible irrational number

[magic bison]

It is preknown value by calculating

[gray patio]

in calculator it say 1.861353...

[modern sedge]

yep

[gray patio]

wat do i do now

[magic bison]

For example log base 10 of 2 is 0.31

[modern sedge]

focus on whole expression instead of just parts of it

[gray patio]

so u need to simplify the expression first?

[modern sedge]

I would start by evaluating this part

[gray patio]

n than calculate it

[modern sedge]

this can be computed by hand tho

[gray patio]

ye dis look s1mple

[modern sedge]

remember definition of log, to what power do you have to raise 5 to get 5^(-1)?

[magic bison]

Actually if you don't know what is computable by hand just use multiplication and division and simplify it

[gray patio]

1

?

[gray patio]

right?

wat u deal w negative log than

[modern sedge]

Oh wait did you calculate just the log or did you include that -

[gray patio]

ofc including dat -

[modern sedge]

this one?

[ocean seal]

MathIsAlwaysRight

[gray patio]

eh

yes

[modern sedge]

if so then yes, good job it's correct

[gray patio]

so I got a 1 now

[modern sedge]

$\log_{5}\left(20\right)+\log_{5}\left(\frac{125}{4}\right)+1$

[ocean seal]

MathIsAlwaysRight

[modern sedge]

so now you are left with this

[gray patio]

wat do I do for 2 of the expression b4

damn

no idea

[modern sedge]

Notice that there is a fraction in one of the logs

[gray patio]

ye

[modern sedge]

can you break it down using that rule?

[gray patio]

which ruel

rule

[modern sedge]

pick one, and see if you can apply it

[gray patio]

third one?

[modern sedge]

yep

[gray patio]

ok let

c

wait

hold up

how abt the base

it dissapear

from that pic

[modern sedge]

those rules works for every base

[gray patio]

nonono I mean log_5(fraction)

but in that thing there is no basew

it just log(fraction)

no _5

or _n

[modern sedge]

yeah, if you use base 5 then those logs are all with base 5

[gray patio]

oh ok

how u deal w log_5(4)

it decimal

[modern sedge]

yeah, hard to deal with that one. So just keep in

anyways you probably got log_5(125)-log_5(4)

can you simplify that by evaluating log_5(125)?

[gray patio]

wat

there is no power of 5 that include 125?

or is there

[modern sedge]

5^1=5

5^2=25

[gray patio]

oh

[modern sedge]

5^3=125
5^4=625

[gray patio]

got it

yes

so it equal 3

[modern sedge]

yep

[gray patio]

so 3-log_5(4)+1

[modern sedge]

yeah, and also the log_5(20)

[ocean seal]

MathIsAlwaysRight

[modern sedge]

so you now have this, I also simplified it a bit by adding 1 to 3

[gray patio]

right

[modern sedge]

time for another rule to simplify log_5(20)

[gray patio]

which rule

I c none of them in there

[modern sedge]

notice that 20 can be written as product of 2 numbers

or even 3 numbers

[gray patio]

20 = 225

[modern sedge]

yep

[gray patio]

2 * 2 * 5

so.

[modern sedge]

watch also the right sides of the rules

[gray patio]

it mean dat equal log_5(4 * 5)

[modern sedge]

yep

[gray patio]

which equal to log_5(4) + log_5(5)

[modern sedge]

yep

and log_5(5) is?

[gray patio]

1

[modern sedge]

$\log_{5}\left(4\right)+1-\log_{5}\left(4\right)+4$

[ocean seal]

MathIsAlwaysRight

[modern sedge]

so now you have this

[gray patio]

wait

I think u missing another 1

oh I mean

no

ye u gud

[modern sedge]

I added it to 3

[gray patio]

ok so now I have left w log_5(4)-log_5(4)+5

[modern sedge]

yep

[gray patio]

which = 5

wow

[modern sedge]

exactly

[gray patio]

quality

how we deal w dis than

logq

wat is dat

[modern sedge]

log without base usually reffers to log base 10

[gray patio]

wat?

[modern sedge]

log(x)=log_10(x)

just fyi

[gray patio]

so log(2) = log_10(2)

[modern sedge]

yep, it usually reffers to it

[gray patio]

wdym,= usually

how abt other

unusually

[modern sedge]

depends on context, in more advanced mathematics it sometimes reffers to log base e

[gray patio]

e???

wat even is dat

[modern sedge]

e is a special number around 2.718

[gray patio]

wat does it represent

kind of like pi?

or smth

abt triangle???

[modern sedge]

yeah, constant like pi. If I gave you 1$ and and on end of year I would add 100% of that, you would have 2$ in a year. If I instead gave you 50% twice, you would have 1.5$ and then the another 50% would be 1.5 + 50% of the 1.5$ which is 2.25$. And if I instead gave you 100/infinity% infinity times, you would have e$ at the end

[gray patio]

wut???

how

if u give me 50% 2 times than it 100%

than I still got 1 buck

u there bud

eh

[modern sedge]

you would have 1$ and I would give you 50% of that in addition. So you would have 1.5$

[gray patio]

yes

[modern sedge]

and then I would give you another 50%, but this time of the 1.5$

[gray patio]

and u give me another 50% of 1 buck

wat

so it like dis

[modern sedge]

yeah, like that

sorry if it was confusing

[gray patio]

(100%+50%)+50%

so it means that I would get 2.25

than if like that the number will be infinite at the end

since it adding up

ehh

is it abit over??

should I just stick w my grade lvl stuff